Simplify: ${(x^{a})}^{b + c} {(x^{b})}^{c + a} {(x^{c})}^{a + b}$

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Solution

given, ${(x^{a})}^{b + c} {(x^{b})}^{c + a} {(x^{c})}^{a + b}$

$= (x^{a b + a c}) (x^{b c + b a}) (x^{c a + c b})$

$= x^{a b + a c + b c + b a + c a + c b}$

$= x^{2 a b + 2 b c + 2 c a}$

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